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We present a mathematical derivation of a closure relating the Reynolds stress to the mean strain rate for incompressible flows.
The mean strain rate varies linearly with the turbulent intensity, but shows no noticeable dependence on the Lewis number.
As the complex relationships between fracture life and its influencing factors can be well explained by the mean strain rate at half-life, which is considered as the main factor associated with the fracture life.
Spatial distributions of the grid scale turbulent kinetic energy (kGS) and mean strain rate (Sij) were obtained from the LES results, and the value of the turbulent length scale was estimated from the kGS and Sij values.
This scaling rule also applies to flames submitted to a time-variable strain rate provided that the frequencies characterizing these changes are low compared to the mean strain rate.
In all cases when the oscillation amplitude is normalized by the cycle mean strain rate and plotted against the non-dimensional flow field frequency, the results collapse onto a single line having a steep negative slope.
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Mean strain rates, conditioned on the CH-peak contour, are relatively constant (150 s−1) in the Re = 9100 flame and increase (650 1700 s−1) with axial location in the Re = 18,600 flame, resulting from the flame wrinkling process.
Furthermore, this 3D FGM accurately predicts a broad range of the strain-rate parameters: the mean strain-rate, the applied amplitude, and the frequency of the sinusoidally varying strain-rate.
Schneider et al. suggested using mean strain and strain rate values measured during systole (LAs) and at early (LAe) and late (LAa) diastole as indicators of reverse atrial remodeling.
Strains with great short-distance dispersal rates in presence of nutrients had a better growth performance, and high colonization abilities as predicted ([ 30, 31, 79] but see [ 80]), but contrary to classical predictions they also had a better mean strain survival rate than did less dispersive strains.
The stability limits were determined through the observation of flame merging and flame extinction, a function of rich and lean equivalence ratios, and mean axial strain rate.
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